Abstract <p>This work aims to construct a phenomenological model of a multiphase multicomponent chemically active continuous medium, within which gas–liquid satellites of the giant planets of the Solar System can comprehensively be studied. With this approach, specialized models of individual dynamic, physical, and chemical processes in the water oceans of these cosmic objects can be integrated into a single whole, i.e., this approach takes into account their complexity and mutual influence, inducing significant mutual changes. A heterogeneous continuum model has been developed for multilayer nonperfect media with the methods of multivelocity mechanics and nonequilibrium thermodynamics, accounting for the asymmetry of the pressure tensor of phase media, equilibrium chemical reactions, phase transitions, and heat- and mass-transfer processes. The generalized Stefan–Maxwell relations for multiphase mixtures, which are a system of equations of motion of individual phases with genuine inertial forces, have been first derived in terms of thermodynamics. We propose a thermodynamic technique that allows obtaining a number of algebraic relationships for transport coefficients associated with diffusion–thermal processes in a multiphase medium. The developed approach is primarily intended for mathematical modeling of the water ocean and ice crust of Saturn’s moon Enceladus, beneath the surface of which one could possibly search for extraterrestrial life in the Solar System.</p>